Contents
dtrexc - reorder the real Schur factorization of a real
matrix A = Q*T*Q**T, so that the diagonal block of T with
row index IFST is moved to row ILST
SUBROUTINE DTREXC(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO)
CHARACTER * 1 COMPQ
INTEGER N, LDT, LDQ, IFST, ILST, INFO
DOUBLE PRECISION T(LDT,*), Q(LDQ,*), WORK(*)
SUBROUTINE DTREXC_64(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
INFO)
CHARACTER * 1 COMPQ
INTEGER*8 N, LDT, LDQ, IFST, ILST, INFO
DOUBLE PRECISION T(LDT,*), Q(LDQ,*), WORK(*)
F95 INTERFACE
SUBROUTINE TREXC(COMPQ, N, T, [LDT], Q, [LDQ], IFST, ILST, [WORK],
[INFO])
CHARACTER(LEN=1) :: COMPQ
INTEGER :: N, LDT, LDQ, IFST, ILST, INFO
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: T, Q
SUBROUTINE TREXC_64(COMPQ, N, T, [LDT], Q, [LDQ], IFST, ILST, [WORK],
[INFO])
CHARACTER(LEN=1) :: COMPQ
INTEGER(8) :: N, LDT, LDQ, IFST, ILST, INFO
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: T, Q
C INTERFACE
#include <sunperf.h>
void dtrexc(char compq, int n, double *t, int ldt, double
*q, int ldq, int *ifst, int *ilst, int *info);
void dtrexc_64(char compq, long n, double *t, long ldt, dou-
ble *q, long ldq, long *ifst, long *ilst, long
*info);
dtrexc reorders the real Schur factorization of a real
matrix A = Q*T*Q**T, so that the diagonal block of T with
row index IFST is moved to row ILST.
The real Schur form T is reordered by an orthogonal similar-
ity transformation Z**T*T*Z, and optionally the matrix Q of
Schur vectors is updated by postmultiplying it with Z.
T must be in Schur canonical form (as returned by SHSEQR),
that is, block upper triangular with 1-by-1 and 2-by-2 diag-
onal blocks; each 2-by-2 diagonal block has its diagonal
elements equal and its off-diagonal elements of opposite
sign.
COMPQ (input)
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
N (input) The order of the matrix T. N >= 0.
T (input/output)
On entry, the upper quasi-triangular matrix T, in
Schur Schur canonical form. On exit, the reor-
dered upper quasi-triangular matrix, again in
Schur canonical form.
LDT (input)
The leading dimension of the array T. LDT >=
max(1,N).
Q (input) On entry, if COMPQ = 'V', the matrix Q of Schur
vectors. On exit, if COMPQ = 'V', Q has been
postmultiplied by the orthogonal transformation
matrix Z which reorders T. If COMPQ = 'N', Q is
not referenced.
LDQ (input)
The leading dimension of the array Q. LDQ >=
max(1,N).
IFST (input/output)
Specify the reordering of the diagonal blocks of
T. The block with row index IFST is moved to row
ILST, by a sequence of transpositions between
adjacent blocks. On exit, if IFST pointed on
entry to the second row of a 2-by-2 block, it is
changed to point to the first row; ILST always
points to the first row of the block in its final
position (which may differ from its input value by
+1 or -1). 1 <= IFST <= N; 1 <= ILST <= N.
ILST (input/output)
See the description of IFST.
WORK (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
= 1: two adjacent blocks were too close to swap
(the problem is very ill-conditioned); T may have
been partially reordered, and ILST points to the
first row of the current position of the block
being moved.